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Accurate prediction method of initial value of high-speed ball bearing model and gyroscopic torque analysis

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Abstract

An accurate prediction method of initial value of high-speed ball bearing model is studyed and its gyroscopic torque is analyzed. First, a new iterative algorithm for high-speed ball bearings is proposed, in which the effects of gyroscopic torque and centrifugal force are considered. Then, to accurately predict the initial values for the proposed iterative algorithm, the combined displacements of bearings are calculated as the initial values according to the deformation superposition principle. The general applicability of this new iterative algorithm for high-speed ball bearings is demonstrated. Subsequently, the effects of combined loads, rotational speed, moment, and raceway groove curvature radius on the gyroscopic torque are discussed in detail. The results provide valuable guidelines for the reasonable selection of combined loads, rotational speed, and raceway groove curvature radii.

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Abbreviations

D :

Ball diameter (mm)

r :

Raceway groove curvature radius (mm)

f :

r/D

F :

Force (N)

F c :

Centrifugal force (N)

M :

Moment (Nm)

α 0 :

Initial contact angle (0)

ℜ:

Radius of locus of raceway groove curvature centers (mm)

θ :

Angular displacement (rad)

ψ :

Position angle of ball (0)

δ :

Deflection or contact deformation (mm)

X 1 :

Axial projection of distance between ball center and outer raceway groove curvature center (mm)

X 2 :

Radial projection of distance between ball center and outer raceway groove curvature center (mm)

Q:

Ball normal load (N)

α :

Contact angle (0)

M g :

Gyroscopic moment (Nm)

β :

Ball pitch angle (0)

d m :

Pitch diameter (mm)

Y′:

D/d m

m :

Ball mass (kg)

J :

Mass moment of inertia (kg/m2)

ω :

Rotational speed (rad/sec)

ω m :

Orbital speed of ball (rad/sec)

ω R :

Speed of ball about its own axis(rad/sec)

ξ 1 :

Changed contact angle at axial force

ξ 2 :

Changed contact angle at combined forces

Z :

Ball number

K :

Load-deflection factor

c :

Contact deformation coefficient

ε :

Ball load distribution parameter

a :

Axial direction

r :

Radial direction

j :

Ball at angular location

i :

Inner raceway

o :

Outer raceway

p :

Point contact

n :

Direction collinear with normal load

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Acknowledgments

The authors would like to thank the National Natural Science Foundation of China (No. 51605354), the Overseas Expertise Introduction Center for Discipline Innovation (No. B17034) and the Major Program of Science and Technology Program of Hubei Province (No. 2018AAA030) for the support given to this research.

Author information

Authors and Affiliations

  1. School of Automotive Engineering, Hubei Key Laboratory of Advanced Technology of Automotive Parts, Wuhan University of Technology, Wuhan, 430070, China

    Lina Hao, Song Deng & Lin Hua

  2. Hubei Collaborative Innovation Center for Automotive Components Technology, Wuhan University of Technology, Wuhan, 430070, China

    Lina Hao, Song Deng, Dongsheng Qian & Lin Hua

  3. School of Materials Science and Engineering, Wuhan University of Technology, Wuhan, 430070, China

    Dongsheng Qian

Authors
  1. Lina Hao
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  2. Song Deng
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  3. Dongsheng Qian
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  4. Lin Hua
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Corresponding author

Correspondence to Song Deng.

Additional information

Lina Hao is currently a graduate student majoring in Mechanical Engineering at the School of Automotive Engineering, Hubei Key Laboratory of Advanced Technology of Automotive Components at Wuhan University of Technology, China. Her research areas include structure design and dynamic behavior of high-speed bearing.

Dongsheng Qian received his Ph.D. degree in Mechanical Engineering from Wuhan University of Technology, China, in 2009. Qian is currently a Professor at the School of Materials Science and Engineering, Hubei Key Laboratory of Advanced Technology of Automotive Components at Wuhan University of Technology, China.

Song Deng received his Ph.D. degree in Vehicle Engineering from Wuhan University of Technology, China, in 2014. Deng is currently an Associate Professor at the School of Automotive Engineering, Hubei Key Laboratory of Advanced Technology of Automotive Components at Wuhan University of Technology, China. His research areas include structure design and dynamic behavior of high-speed bearing.

Lin Hua received his Ph.D. degree in Mechanical Engineering from Xi’an Jiaotong University, China, in 2002. Dr. Hua is currently a Professor at the School of Automotive Engineering, Hubei Key Laboratory of Advanced Technology of Automotive Components at Wuhan University of Technology, China. Dr. Hua’s research interests include advanced manufacturing technology.

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Hao, L., Deng, S., Qian, D. et al. Accurate prediction method of initial value of high-speed ball bearing model and gyroscopic torque analysis. J Mech Sci Technol 34, 3745–3755 (2020). https://doi.org/10.1007/s12206-020-0826-8

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  • DOI: https://doi.org/10.1007/s12206-020-0826-8

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